U.K. Prime Minister Theresa May has told ministers to show "strength and unity", and to keep details of their discussions private, after reports over the weekend suggested divides over Brexit.

One of those reports involved an unnamed minister allegedly accusing U.K. finance minister Philip Hammond of trying to "f--- up" the country's departure from the European Union.

"There is a need to show strength and unity as a country and that starts around the cabinet table," Mrs May said on Tuesday, according to a government spokesperson.

May's government suffered a weakened majority in last month's election, and tensions have been heightened further over whether the country should remain in the EU single market or face a "hard Brexit" outside of it.

Hammond welcomes 'any opportunity to build consensus'

Chancellor Hammond told U.K. parliamentarians that he welcomed any opportunity to reach consensus on Britain's divorce from the EU.

"In an issue as important to our nation's future as our exit from the European Union, I welcome any opportunity to build consensus across the House (Parliament) and across the nation," Hammond said on Tuesday.

Responding to the damaging leaks – one of which referred to him as "an enfeebled chancellor" – he added: "I don't feel particularly enfeebled."

"My focus is ensuring that we get a Brexit deal that protects our existing patterns of trade and commercial engagement with the European Union, as well as over time allowing us to explore new opportunities beyond the European Union," Hammond said.

More From CNBC

• Fears over a government collapse leave investors weighing chances of another UK election
  

• UK PM Theresa May shed a 'little tear' over election failure
  

• Theresa May is a leader on borrowed time: Lord Patten